physics trajectory problem

Upon spotting an insect on a twig overhanging water, an archer fish squirts water drops at the insect to knock it into the water. Although the fish sees the insect along a straight-line path at angle φ and distance d, a drop must be launched at a different angle θ0 if its parabolic path is to intersect the insect. If φ = 38.0° and d = 0.900 m what θ0 is required for the drop to be at the top of the parabolic path when it reaches the insect?

Just poking at the problem I have found that the height of the insect is .55m.

If i plug the height into the max height formula, i get velocity at time 0 = 5.33m/s

I am not sure if this is even right, or if I am on the right track.

I dont feel like enough info is given.

Any ideas?

Quote:

Originally Posted by silencecloak

Upon spotting an insect on a twig overhanging water, an archer fish squirts water drops at the insect to knock it into the water. Although the fish sees the insect along a straight-line path at angle φ and distance d, a drop must be launched at a different angle θ0 if its parabolic path is to intersect the insect. If φ = 38.0° and d = 0.900 m what θ0 is required for the drop to be at the top of the parabolic path when it reaches the insect?

Just poking at the problem I have found that the height of the insect is .55m.

If i plug the height into the max height formula, i get velocity at time 0 = 5.33m/s

I am not sure if this is even right, or if I am on the right track.

Quote:

Originally Posted by silencecloak

I dont feel like enough info is given.

Any ideas?

In the vertical direction you know that a = -9.8 m/s^2, final velocity = 0 (because you're at the top of the parabolic path) and x = 0.55 m (I didn't check this value by the way). Calculate t using an appropriate uniform acceleration formula.

Now substitute a = -9.8 m/s^2, final velocity = 0, x = 0.55 m and initial velocity $= u \sin \theta$ into an appropriate uniform acceleration formula. Call this equation (1).

In the horizontal direction you know that a = 0, x = ...., t = (calculated above) and initial velocity $= u \cos \theta$ . Substitute into an appropriate uniform acceleration formula. Call this equation (2).

Now solve equations (1) and (2) simultaneously for $\theta$ .